I think you are intentionally misquoting the section about PAC learning of Aaronson's paper, in order to ask a question about that nicely written paper.
The intention of the quoted section is not to prove Occam's razor, but to explain how Valiant's theory of PAC learning can help with clarifying the following questions regarding Occam's razor:
(1) What do we mean by “simpler”?
(2) Why are simple explanations likely to be correct? Or, less ambitiously: what properties must reality have for Occam’s Razor to “work”?
(3) How much data must we collect before we can find a “simple hypothesis” that will probably predict future data? How do we go about finding such a hypothesis?
The drawback related to the i.i.d. assumption is sufficiently highlighted in the same section:
The third drawback of Theorem 2 is the assumption that the distribution D from which the learner is tested is the same as the distribution from which the sample points were drawn. To me, this is the most serious drawback, since it tells us that PAC-learning models the “learning” performed by an undergraduate cramming for an exam by solving last year’s problems, or an employer using a regression model to identify the characteristics of successful hires, or a cryptanalyst breaking a code from a collection of plaintexts and ciphertexts.
Even so I only read that paper in order to be entitled to answer this question, I think the paper is really worth reading even if you don't want to answer any question. It's easy to read, covers much ground, and even sketches the proofs for some non-obvious theorems. But is it relevant to philosophy? Well, it is an honest attempt to address an audience of philosophers and tries to reduce (or show how it might be possible to reduce) the gap between theory and reality in certain areas.